280 PHILOSOPHICAL TKANSACTIONS. [anNO 1739- 



Poleni's experiments seem to be preferable to all others, not only because of 

 his extraordinary diligence and accuracy, but on other accounts also. He 

 found, that the quantity of water flowing out of a vessel through a cylindrical 

 tube, far exceeded that which flowed through a circular hole made in a thin 

 plate, the tube and hole being of equal diameter, and the height of the water 

 over both being also equal. And he found it to be so, when the tube was in- 

 serted, not only into the bottom, which others had observed before, but also into 

 the side of the vessel. 



Now a hole made in the thinnest plate must be considered as a short cylin- 

 drical tube. Whence it appears that a greater quantity of water runs through 

 a hole made in a thin plate, than would have run out, if the thickness of the 

 plate had been what is called infinitely small. But as such a plate can neither 

 exist, nor even be conceived by the imagination, it remains that we increase 

 the diameter of the hole, that the thickness of the plate may bear the least 

 proportion possible to that diameter. 



This Poleni performed with great judgment, when he made use of a diameter 

 of 26 lines, and not quite a line thick ; whereas before him hardly any one 

 made use of a diameter of above 6 or 7 lines, or ever attended to the thickness 

 of the plate or bottom of the vessel, except Sir I. Newton, who mentions his 

 making use of a very thin plate. But Poleni exceeded all others, in consider- 

 ing not only the size of the hole, but of the vessel also, that the water might 

 descend toward the hole with the greatest freedom, and the least impediment ; 

 so that there can be no doubt but that the measures taken by him, come much 

 nearer the truth than any other. 



6. Since then the measure of the water running out in the abovementioned 

 time T, is 2af X toVs-* the length of the column of water, which runs out 

 in that time, is 2a X -nrgV- Therefore if each of the particles of water, 

 which are in the hole in the same space of time, passes with equal velocity, it 

 is plain that the common velocity of them all, is that which the space 2a X 

 would be gone over in the time t, or the velocity v x , Vo'o • But this 







is the velocity with which water could spring or jet in vacuo to near ^ of the 

 height of the water above the hole. 



7. But when the motion of water is turned upwards, as in fountains, these 

 are seen to rise almost to the whole height of the water in the cistern. There- 

 fore the water, or at least some portion of it, spouts from the hole with 

 almost the whole velocity v, and certainly with a much greater velocity than 



V y\ 1 « • 



8. Hence it is evident, that the particles of water which are in the hole at 

 the same point of time, do not all burst out with the same velocity, or they 



